This dissertation presents a method that can be used to identify the
parameters of a class of systems whose regressor models are nonlinear in the
parameters.
The technique is based on classical elimination theory, and it guarantees
that the solution for the parameters which minimize a least-squares criterion can
be found in a finite number of steps. The proposed methodology begins with an
input-output linear overparameterized model whose parameters are rationally
related. After making appropriate substitutions that account for the
overparameterization, the problem is transformed into a nonlinear least-squares
problem that is not overparameterized. The extrema equations are computed, and
a nonlinear transformation is carried out to convert them to polynomial equations
in the unknown parameters. It is then show how these polynomial equations can
be solved using elimination theory using resultants. The optimization problem
reduces to a numerical computation of the roots of a polynomial in a single
variable.
This nonlinear least-squares method is applied to the identification of the
parameters of an induction motor. A major difficulty with the induction motor is
that the rotor’s state variables are not available measurements so that the system
identification model cannot be made linear in the parameters without
overparameterizing the model. Previous work in the literature has avoided this
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issue by making simplifying assumptions such as a “slowly varying speed”. Here,
no such simplifying assumptions are made. This method is implemented online to
continuously update the parameter values. Experimental results are presented to
verify this method.
The application of this nonlinear least-squares method can be extended to
many research areas such as the parameter identification for Hammerstein
models. In principle, as long as the regressor model is such that the system
parameters are rationally related, the proposed method is applicable.
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